D-Optimal Three-Stage Unbalanced Nested Designs for the Determination of Measurement Precision

Abstract

The precision of measurement results can be quantified by variance components of random effect models. The variance components are estimated from measurement results that are obtained by performing a collaborative assessment experiment. The measurement results are statistically modeled by a nested design. Although balanced nested designs are widely used, staggered nested designs, which are one type of unbalanced nested designs, have the statistical advantage that the degrees of freedom in all stages except for the top stage are equal. Thus, balanced nested designs do not necessarily have a better performance from the statistical point of view. In this study, D-optimal designs are identified in general nested designs that include both balanced and unbalanced designs and consider the practical feasibility of collaborative assessment experiments as well.